Answer:
The angle of separation is [tex]\Delta \theta = 0.93 ^o[/tex]
Explanation:
From the question we are told that
The angle of incidence is [tex]\theta _ i = 56^o[/tex]
The refractive index of violet light in diamond is [tex]n_v = 2.46[/tex]
The refractive index of red light in diamond is [tex]n_r = 2.41[/tex]
The wavelength of violet light is [tex]\lambda _v = 400nm = 400*10^{-9}m[/tex]
The wavelength of red light is [tex]\lambda _r = 700nm = 700*10^{-9}m[/tex]
Snell's Law can be represented mathematically as
[tex]\frac{sin \theta_i}{sin \theta_r} = n[/tex]
Where [tex]\theta_r[/tex] is the angle of refraction
=> [tex]sin \theta_r = \frac{sin \theta_i}{n}[/tex]
Now considering violet light
[tex]sin \theta_r__{v}} = \frac{sin \theta_i}{n_v}[/tex]
substituting values
[tex]sin \theta_r__{v}} = \frac{sin (56)}{2.46}[/tex]
[tex]sin \theta_r__{v}} = 0.337[/tex]
[tex]\theta_r__{v}} = sin ^{-1} (0.337)[/tex]
[tex]\theta_r__{v}} = 19.69^o[/tex]
Now considering red light
[tex]sin \theta_r__{R}} = \frac{sin \theta_i}{n_r}[/tex]
substituting values
[tex]sin \theta_r__{R}} = \frac{sin (56)}{2.41}[/tex]
[tex]sin \theta_r__{R}} = 0.344[/tex]
[tex]\theta_r__{R}} = sin ^{-1} (0.344)[/tex]
[tex]\theta_r__{R}} = 20.12^o[/tex]
The angle of separation between the red light and the violet light is mathematically evaluated as
[tex]\Delta \theta = \theta_r__{R}} - \theta_r__{V}}[/tex]
substituting values
[tex]\Delta \theta =20.12 - 19.69[/tex]
[tex]\Delta \theta = 0.93 ^o[/tex]
